How to Bend it like Beckham: Calculating the Perfect Football Formula

Now that David Beckham won't be appearing at the London 2012 Olympics, other members of Team GB wanting to brush up on their free-kicks can rest easy. University of Leicester physics students have published a paper that sets out the optimum way of kicking a football in order to make it bend into the goal.

The ex-England captain's curling free-kicks became legendary, and even inspired the title of the 2002 film Bend It Like Beckham.

Now, four master's students at the University of Leicester's Department of Physics and Astronomy believe they have discovered a formula to explain how the football curves when a player puts spin on it.

Jasmine Sandhu, Amy Edgington, Matthew Grant and Naomi Rowe-Gurney found a relationship between the amount a football bends in the air, the speed it is travelling and the angular velocity — or "spin" — applied to the ball.

When a football spins in the air, it is subjected to a force called the Magnus force — which causes it to curl sideways from the direction it was originally kicked.

The group found that the distance a ball bends (D) as a result of this force is related to the ball's radius (R), the density of air (?), the ball's angular velocity (?), it's velocity through the air (v), it's mass (m) and the distance travelled by the ball in the direction it was kicked (x).

They found that the various parts can be tied together using this formula:

For instance, if a player standing 15 meters away from the byline kicked an average football so that it was travelling at a velocity of 35 meters per second and had an angular velocity of 10 revolutions per second, the ball would bend around 5 meters towards the goal.

As a result, the player would probably need to bring a tape measure — as well as a measure of their own abilities — if they wanted to put the theory into practice during a game!

Jasmine Sandhu, 22, who studies Physics with Space Science and Technology, said: "Whilst researching new ideas for a paper, I read about how physics influences various aspects of football, from the clothing they wear to the effects of playing at high altitude.

"The article discussed how a new design of ball, used in the 2010 World Cup, has three dimensional moulding of the panels in order to produce a more rounded ball, thus affecting the spin that can be imparted.

"This prompted us to examine how footballers use spin on the ball, and the factors which influence how much the path of the ball would bend.

"These findings made me more aware of how I can use spin to bend the ball in a game of football. In addition, this research is also relevant to other sports, such as tennis, which shows that physics definitely gives you the edge!"

The paper was published in this year's University of Leicester Journal of Special Physics Topics, which features original short papers written by students in the final year of their four-year Master of Physics degree.

Course leader Dr. Mervyn Roy, a lecturer at the University's Department of Physics and Astronomy, said: "A lot of the papers published in the journal are on subjects that are amusing, topical, or a bit off-the-wall. Our fourth years are nothing if not creative! But, to be a research physicist — in industry or academia — you need to show some imagination, to think outside the box, and this is certainly something that the module allows our students to practice.

"Most of our masters students hope to go on to careers in research where a lot of their time will be taken up with scientific publishing — writing and submitting papers, and writing and responding to referee reports.

"This is another area where the module really helps. Because Physics Special Topics is run exactly like a professional journal, the students get the chance to develop all the skills they will need when dealing with high profile journals like Nature or Science later on in life."